Thanks for the clarification.

It could be 10+ years of me misremembering the explanation. The person who told me this was Korean, so it seems more likely that I misremembered than them explaining it wrong.

You're pretty much there. Oppa is literally 'older brother' but is generally used towards a man who is older but within the same age-hierarchy bracket. It is a term exclusively used by women, except for when men are referring to themselves in the 3rd person from the perspective of women. As mentioned, women often call their boyfriend/husband oppa in casual environments.

The lyrics of the chorus is "오빤 강남 스타일" ("Oppan Gangnam Style") where the 'n' after 'oppa' is like a contraction of "오빠는" ('Oppa nun' / "Oppa is"). Gangnam is a neighborhood in Seoul where literal 1%ers live. So he's basically letting the women know he's a wealthy/noteworthy/powerful guy, since he is 'Gangnam Style'.

In truth, the way he describes himself and the women he chases are caricatures of South Korean wealth, materialism, and high-class identity. The video starts with him pretending to be at a beach, when the camera pans out it's actually a sandlot for a playground. More examples of his phony elegance show up across the video, such as dancing on a tour bus and singing in a toilet stall. The lyrics of the song flaunt the lavish lives of the hyper-wealthy, while the imagery points out how trashy and narcissistic that kind of lifestyle can be.

Sorry for the rant, I just remember a lot of stuff I learned about it while writing a report in high school. I hope someone learned something :P